共查询到20条相似文献,搜索用时 31 毫秒
1.
Dr. Erhard Braune 《Monatshefte für Mathematik》1976,82(1):17-26
Let (itk) (s) denote thek-th derivative of the Riemann Zeta-function,s=+it, ,t real numbers,k1 rational integers. Using ideas fromT. C. Titchmarsh and from a paper ofR. Spira, lower bounds are derived for |(itk)(s)|, |(itk)(1-s) for >1 and some infinitely many, sufficiently large values oft. Further let be an algebraic number of degreen and heightH; then a lower bound for |(itk)(its)|, dependent onn, H, k is established for alln,H1,k3, 2+7k/4 and all realt. 相似文献
2.
Alberto Marcone 《Order》2001,18(4):339-347
We pursue the fine analysis of the quasi-orderings
and
on the power set of a quasi-ordering (Q,). We set X
Y if every xX is majorized in by some yY, and X
Y if every yY is minorized in by some xX. We show that both these quasi-orderings are -wqo if and only if the original quasi-ordering is ( )-wqo. For
this holds also restricted to finite subsets, thus providing an example of a finitary operation on quasi-orderings which does not preserve wqo but preserves bqo. 相似文献
3.
С. С. Волосивец 《Analysis Mathematica》1995,21(1):61-77
A new discrete modulus of continuity is introduced for functions of boundedp-fluctuation, and direct and converse theorems are proved on the approximation of these functions by polynomials with respect to multiplicative systems. Sufficient conditions for the convergence of Fourier series with respect to multiplicative systems are also obtained and these are the best possible in a certain sense.
. 60- 相似文献
. 60- 相似文献
4.
V. G. Alekseev 《Journal of Mathematical Sciences》1993,67(4):3149-3152
The symmetry properties of the spectral densitiesf
(v)() of order v, equal to 4, 5, and 6 of a stationary stochastic process {(k), k Z} are studied. It is established that the fonctionf
(v)(), Rv–1 is completely determined by its values on a set whose (v– 1)-dimensional volume is 4/6, 5/15, and 5/45 when v is equal to 4, 5, and 6, respectively. Results on the statistical estimation of the spectral densities of orders v equal to 3 and 4 with respect to samples of finite size are also given.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 1–4, 1988. 相似文献
5.
Summary Let be a probability measure on a separable locally convex Fréchet space E and let s
denote the topology on E of the convergence in . Then (E, s
) is nuclear iff ((E', s
))=1. 相似文献
6.
We prove a local limit theorem (LLT) on Cramer-type large deviations for sums S
V
=
t
V (
t
), where
t
, t Z
, 1, is a Markov Gaussian random field, V Z
, and is a bounded Borel function. We get an estimate from below for the variance of S
V
and construct two classes of functions , for which the LLT of large deviations holds. 相似文献
7.
We investigate the motion of high-energy particles in a crystal with regard to their interaction with the thermal vibrations of the lattice atoms using analytic methods in the theory of Markov processes including the local Fokker–Planck equation. We construct a local matrix of random actions, which is used to introduce the main kinetic functions in the traverse-energy space, namely, the function a() of energy losses due to the dynamic friction and the diffusion function b(). We show that the singularities of the functions a() and b() are related to the distinction between the contributions to the kinetics from particles moving in three different regimes, namely, in the channeling, quasichanneling, and chaotic motion modes. 相似文献
8.
Summary We investigate generalizations of the classical Jensen and Chebyshev inequalities. On one hand, we restrict the class of functions and on the other we enlarge the class of measures which are allowed. As an example, consider the inequality (J)(f(x) d) A (f(x) d, d d = 1. Iff is an arbitrary nonnegativeL
x
function, this holds if 0, is convex andA = 1. Iff is monotone the measure need not be positive for (J) to hold for all convex withA = 1. If has higher monotonicity, e.g., is also convex, then we get a version of (J) withA < 1 and measures that need not be positive. 相似文献
9.
Delaunay Transformations of a Delaunay Polytope 总被引:1,自引:0,他引:1
Monique Laurent 《Journal of Algebraic Combinatorics》1996,5(1):37-46
Let P be a Delaunay polytope in
n
. Let T(P) denote the set of affine bijections f of
n
for which f (P) is again a Delaunay polytope. The relation: fg if f, g differ by an orthogonal transformation and/or a translation is an equivalence relation on T(P). We show that the dimension (in the topological sense) of the quotient set T(P)/ coincides with another parameter of P, namely, with its rank.Let V denote the set of vertices of P and let dp denote the distance on V defined by dp(u, v)=u–v
2 for u, vV. Assouad [1] shows that dp belongs to the cone
|V|:={d |
u,vV
b
u
b
v
d(u,v) 0 for b
V
with
uV
b
u
= 1}. Then, the rank of P is defined as the dimension of the smallest face of the cone
|V| that contains dp.
AMS Subject Classification (1991): 11H06, 52C07. 相似文献
10.
V. I. Masol 《Journal of Mathematical Sciences》1993,67(4):3210-3215
Let Js={j1, ..., js} be a collection of nonnegative numbers, j1+...+js=n, js1, R(Js) be the set of sequencesf=(f(1), ...,f(n)) in each of which the integer m occurs js times. Randomly and equiprobably one chooses a sequence f from R(Js). Let n,r be the number of r-drops in f; n be the r-principal index off. Local limit theorems are established in this paper for the random variables n,r and n as n .Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 61–66, 1988. 相似文献
11.
H. X. Phu 《Journal of Optimization Theory and Applications》1995,85(3):649-676
In this paper, the -subdifferential is introduced for investigating the global behavior of real-valued functions on a normed spaceX. Iff: DX attains its global minimum onD atx
*, then 0
f(x
*). This necessary condition always holds, even iff is not continuous orx
* is at the boundary of its domain. Nevertheless, it is useful because, by choosing a suitable +, many local minima cannot satisfy this necessary condition. For the sufficient conditions, the so-called -convex functions are defined. The class of these functions is rather large. For example, every periodic function on the real line is a -convex function. There are -convex functions which are not continuous everywhere. Every function of bounded variation can be represented as the difference of two -convex functions. For all that, -convex functions still have properties similar to those of convex functions. For instance, each -local minimizer off is at the same time a global one. Iff attains its global minimum onD, then it does so at least at one point of its -boundary.This research was supported by the Alexander von Humboldt Foundation. The author thanks Professors R. Bulirsch, K. H. Hoffmann, and H. G. Bock for inviting him to Munich and Augsburg where this research was done. 相似文献
12.
Olivier Rey 《manuscripta mathematica》1989,65(1):19-37
In this paper, we consider the problem: –u=N(N–2)u
p–
, u>0 on ; u=0 on , where is a smooth and bounded domain inR
N, N3, p=
, and >0. We prove a conjecture of H. Brezis and L.A. Peletier about the asymptotic behaviour of solutions of this problem which are minimizing for the Sobolev inequality as goes to zero. We give similar results concerning the related problem: –u=N(N–2)up+u, u>0 on ; u=0 on , for N is larger than 4. 相似文献
13.
Sorin Popa 《Inventiones Mathematicae》1993,111(1):375-405
We construct one parameter families of inclusions of nonhyperfinite type II1 factorsN
s
M
s
, with trivial relative commutant (N
s
)M
s
= and with the Jones' index [M
s
N
s
]=s ranging over the sets{4 cos2/n|n4}[4, ), by using Markov traces on certain universal algebras associated to a given algebra and to the Jones' sequence of projections. This solves the problem of finding all possible values of indices of subfactors with trivial relative commutant in arbitrary type II1 factors, by showing that any numbers>4 can occur.This work was partially supported by an NSF grant DMS-8908281 相似文献
14.
B. Maisonneuve 《Probability Theory and Related Fields》1989,80(3):395-405
Summary Given a random closed setM, adapted to a filtration (
t
), we construct a local time ofM which is both (
t
) adapted and (
Dt
) predictable, whereD
t
=inf{s>t: sM}. Similarly an exit system, both (
t
) optional and (
Dt
) predictable, is associated withM and with the process representing the future at each timet. The paper is motivated by the markovian case, where the general results are applied to Ray processes. 相似文献
15.
Gert K. Pedersen 《Inventiones Mathematicae》1978,45(3):299-305
For each*-derivation of a separableC
*-algebraA and each >0 there is an essential idealI ofA and a self-adjoint multiplierx ofI such that (–ad(ix))|I< and x. 相似文献
16.
For each integer n 2, let
be the index of composition of n, where
. For convenience, we write (1)=(1)=1. We obtain sharp estimates for
and
, as well as for
and
. Finally we study the sum of running over shifted primes.Research supported in part by a grant from NSERC.Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA. 相似文献
17.
Dr. Alexander Kovačec 《Monatshefte für Mathematik》1981,92(1):19-35
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional :
n
, such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map
n
n
, which is functional increasing (i.e. for each x
n
(which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)(
u))(
2(u))...
n
(u)). Under quite general conditions one finds that the sequence {
n
(u)}
n converges tov=v(u). As a consequence one obtains the inequality (u)(v). 相似文献
18.
Wolfgang Grotz 《Monatshefte für Mathematik》1979,88(3):219-228
LetK be an algebraic number field, and for every integer K let () andd(), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (). Asymptotic equalities are proved for the sums () and d
2(), where runs through certain finite sets of integers ofK. 相似文献
19.
Pavlos Tzermias 《Compositio Mathematica》2000,122(3):337-345
This paper is concerned with the arithmetic of curves of the form vp=us(1-u), where p is a prime with p 5 and s is an integer such that 1 s p-2. The Jacobians of these curves admit complex multiplication by a primitive p-th root of unity . We find explicit rational functions on these curves whose divisors are p-multiples of divisors representing (1-)2 - and (1-)3-division points on the corresponding Jacobians. This also gives an effective version of a theorem of Greenberg. 相似文献
20.
Data from a compensatory tracking task are analyzed by using time-domain models. The linear time-domain results are transformed and compared with frequency-domain results. The nonlinear time-domain model of the same data reduced the remnant or residual power by only a small amount. The need for testing models on independent data is discussed. A novel, but attractive, method of generating functions for an efficient functional expansion of time-domain models is offered.Notation
c
Pilot output (control deflection), inches
-
E
Error matrix
-
e
Error, radians
-
F[·]
Fourier transform
-
h
Time interval, seconds
-
h
i
Sample of impulse response of pilot
-
h
p
Impulse response of pilot, inches/radian or inches/degree
-
i
Input (external disturbance function), radians
-
M
Maximum value ofm, M=T
M/
-
m
Index for the argument ofh
p
-
N
Maximum value ofn
-
n
Index for time
-
o
Linear output of pilot model (control deflection), inches
-
r
Remnant signal of pilot model (control deflection), inches
-
S
Matrix
-
s
Laplace variable
-
T
M
Maximum memory time of the pilot model, seconds
-
t
Time, seconds
-
Y
c
Transfer function of controlled element
-
Y
c
j)
Controlled-element transfer function, radians/inch
-
Y
p
j)
Pilot-describing function, inches/radian
-
Argument ofh
p, seconds
-
Incremental value of, seconds
-
Frequency, radians/second
- ^
Estimate
-
Absolute value
-
Phase angle 相似文献